2.3. Integral Properties of Galaxies:
The Physical Meaning of the Hubble Sequence

Classical morphology is useful because it succeeds to some extent
in distinguishing galaxies which are physically different. In particular,
the classification succeeds, although with considerable scatter,
in ranking galaxies by values of physical parameters. The subject of
this section is correlations of integral properties with stage along
the Hubble sequence. By this I will mean the sequence E-S0-a-b-c-d-m-Im
(i.e., the progression toward later types)
(4),
ignoring distinctions
such as that between barred and unbarred galaxies. These most general
correlations of integral properties provide important insight into
galaxy formation problems.

There are two fundamental correlations implicit in the definition
of Hubble types. The first is the decrease in bulge-to-disk ratio B/D
along the Hubble sequence. This is illustrated in
Freeman (1970,
Fig. 9); Yoshizawa and Wakamatsu
(1975,
Fig. 2) and
Boroson (1981,
Fig. 9);
see also
Burstein (1979c);
Dressler (1980b).
[The parameters given in the first two papers and in
Dressler (1980b)
are not true bulge-to-disk
ratios (section 3.4.3), but they
probably order the galaxies by B/D.] All of
these papers show that B/D decreases along the Hubble sequence,
although the intrinsic dispersion is large (see also
Sandage 1961,
1975).
Thus the Hubble sequence is in part a sequence of the decreasing
contribution of an ellipsoidal component which is very centrally
concentrated and which formed stars early in the galaxy collapse phase. A
necessary consequence is that central concentration decreases toward
later types. This correlation is illustrated by photometric concentration
indices
(de Vaucouleurs 1974a,
1977)
and by the decreasing ratio
of galaxy radius to the radius at which the rotation curve peaks or
levels off
(Brosche 1973;
Rubin, Burstein and
Thonnard 1980).
Both of
these correlations persist over the late part of the Hubble sequence
where no bulge is evident. The decrease in central concentration
results in more open spiral arms at later types
(Kennicutt 1981;
see also
Danver 1942);
this is also a classification criterion.

The second fundamental correlation defining the Hubble sequence is
the increasing importance of gas and young stars at later types. The
Hubble sequence is observed to be one of increasingly blue color (e.g.,
van den Bergh 1975a,
after Holmberg 1958;
de Vaucouleurs 1977)
and early spectral type
(de Vaucouleurs 1963,
after
Morgan 1958,
1959).
Also, the mass-to-light ratio within a
Holmberg (1958)
radius decreases toward later types
(Faber and Gallagher
1979,
Fig. 3). Of particular
importance is the fact that the Hubble sequence is one of increasing
H I mass fraction and H I mass-to-(optical)-light ratio (e.g.,
Roberts 1975;
Bothun and Sullivan
1980).
These correlations have led to the
suggestion that the primary factor determining the Hubble stage is the
amount of H I left after disk formation (e.g.,
Sandage, Freeman and
Stokes 1970;
Freeman 1975a).
This is related to the fractional amount
of disk, but not very closely. There are clearly many early-type
galaxies which have little gas but which have structural properties
similar to those of some gas-rich Sc's. The above authors give two
examples of pairs of galaxies with similar structure but very different
gas content and star formation. Apparently, structure and content are
poorly coupled even in field galaxies.

One fundamental parameter which helps to determine Hubble types
appears to be the total mass. It is now clear that the de Vaucouleurs
extension beyond Sc is a sequence of decreasing mass M and
luminosity L.
The total mass is constant or slightly increasing between S0 and Sc,
and then decreases rapidly at later types
(Roberts 1975;
Dickel and Rood 1978;
Faber and Gallagher
1979).
The observable quantity which
leads to this conclusion is the maximum rotation velocity, whose
dependence on type clearly resembles the above correlations
(Brosche 1971).
The correlation of luminosity with type has a maximum at Sbc, and
decreases quite uniformly toward both earlier and later types
(de Vaucouleurs 1963,
1977).
(There are no dwarf Sas or Sbs, but there do exist dwarf S0s and Scs; see
Strom 1980
for a possible interpretation.)
Since M varies little from S0 and Sc, while L increases, the
mass-to-light ratio within a Holmberg radius decreases toward later types
(Faber and Gallagher's
1979
result). This decrease persists to
the end of the Hubble sequence, because L decreases more slowly
than M
beyond Sc. The strong decrease in mass beyond Sc must contribute to
the chaotic structure of very late types, because at low masses there
is less differential rotation to regularize the structure. In
particular, as mass decreases along the sequence Scd-Im, rotation becomes
smaller compared with velocity irregularities of a few 10s of km
s-1,
which are produced by local effects such as stellar winds and supernovae
(see Chevalier 1977;
McCray and Snow 1979;
Conti and McCray 1980;
Silk 1980
for reviews). The details of how structure becomes chaotic
as random motions become comparable to rotation have not been studied.
However, it seems very likely that mass is one fundamental parameter
controlling Hubble stage, although only in the range Sc-Im. The narrow
subdivisions of these late stages give them undue "leverage" in
correlations of integral parameters, leading to suggestions that mass
controls the whole Hubble sequence (e.g.,
Tully, Mould and Aaronson
1982).
This seems unlikely for galaxies of types S0-Sc, although the
surface mass density does decrease systematically even between Sa and
Sc
(Rubin, Ford and Thonnard
1978b).

What is the controlling physical parameter for S0-c galaxies? Why
does galaxy content correlate so poorly with optical structure? A
possible answer is given in a provocative and fundamental paper by
Tinsley (1981).
She shows that the observed decrease of M/L within a
Holmberg radius is much too small to be explained easily by models of
population evolution (Figure 3). Population
models which represent the
observed color spread imply a variation in M/L which is up to ten
times larger than that observed. A careful look at systematic effects in
both the models and the data implies that the difference is significant.
Only if galaxies later than ~ Sbc are all totally dominated by
recent bursts of star formation can the observed M/L - (B-V) relation
be modeled. This is implausible. Tinsley concludes that late-type
galaxies contain proportionally more dark matter than early-type
galaxies. This material is not H I; the H I masses are too small. The
above result is derived with masses measured out to a Holmberg radius.
Dickel and Rood (1978)
and Roberts (1975)
show that total M/L ratios do
not decrease at all toward later types. It appears that the fraction
of the total mass contributed by the halo rises even more rapidly
toward later types than the fraction of the mass within a Holmberg radius.

Figure 3. Mass-to-luminosity ratio versus
color, from
Tinsley (1981).
The mass is calculated within the Holmberg radius; LB
is the total luminosity (from
Faber and Gallagher
1979,
but adjusted to H0 = 100 km s-1
Mpc-1). Data for spiral galaxies are shown as dots,
for S0s as crosses, and for the cores of giant ellipticals as a square.
The curves are for population models in which all mass is in stars
which have the initial mass function of the solar neighborhood.
Different monotonically declining star formation rates (SFR) are used.
The dash-dot curve is for a constant SFR with age increasing toward the
right. The dotted curve is for models of age 5 × 109
yr, with a constant SFR after an initial burst which lasted
109 yr and which
contained 0% of the stars at the red end of the curve and 100% at the
blue end.
The same models at age 1010 yr are shown by the solid curve. All
of the model curves have been shifted upward by factors of ~ 6 in mass
to agree with some of the data. Only if all late-type galaxies are
currently undergoing bursts of star formation is the model curve (not
shown) as shallow as the observed correlation. The implication is that
bluer galaxies have proportionally more dark mass.

Tinsley points out that the above result may mean that the halo
mass fraction is the dominant parameter controlling Hubble types. This
can potentially explain many of the observed correlations. If the
visible part of a galaxy forms inside a fixed halo potential (cf.
White and Rees 1978),
that halo will inhibit star formation, because the gas
is less self-gravitating. If star formation is reduced, inelastic
collisions between clouds will have more time to form a disk. Thus,
increasing the halo contribution tends to lead to a larger disk-to-bulge
ratio, and also to a larger amount of residual gas after disk formation.
Brosche (1973)
has suggested that two parameters control
Hubble types. In late-type galaxies the second parameter may be the
total mass. The second parameter for S0-c galaxies is less clear.
However, the initial distribution of angular momentum per unit mass of
visible galaxy may be important. This, and the more fundamental ratio
of visible galaxy to halo mass might explain why the Hubble sequence is
one of decreasing star formation vigor and increasing dissipation
during galaxy formation. As emphasized by Tinsley, this whole scenario
is very speculative. Also, we need to consider possible alternatives.
For example,
Gunn (1981)
has argued that a galaxy's position in the
Hubble sequence is determined by how much gas it has accreted to form
its disk. Further work is clearly needed. However, the above story is
attractive because the component which contains most of the mass is the
one which controls events.

At the same time, an increase of halo importance toward later
types is a shocking result. The halo is the least dissipational part
of a galaxy. And yet the visible part of the galaxy becomes more
dissipational along the Hubble sequence. This is, there is an
anticorrelation between the two least dissipational components in
galaxies, halos and bulges. This emphasizes the great difference between
halos and the ellipsoidal component. Discontinuities in morphology make
very strong statements. Tinsley's result makes it more difficult to
believe that a halo can be produced by fine-tuning any mechanism that
gives a b ulge or elliptical. Exotic interpretaions of halos become more
credible than they were.

4 If all S0
galaxies are most appropriately thought of as belonging
to a morphological sequence parallel to the Sa-c sequence
(van den Bergh 1976a),
then they should not appear here. It seems likely that
some S0s are formed from spirals while others are true transition
objects between ellipticals and Sas. The latter are relatively more
common in the field. All of the discussion in this section applies
mainly to field galaxies, i.e., to objects which have been affected as
little as possible by environmental processes. I therefore include S0s
in the Hubble sequence. This choice actually makes little practical
difference, since S0s (and also ellipticals) are largely absent from
published parameter correlations.

Almost all of the discussion of this section becomes much more
complicated if morphological types are commonly modified by violent
events (interactions, mergers, nuclear activity, etc.) This is
particularly true of galaxies in rich clusters, and, in fact, the parameter
correlations with Hubble stage have large intrinsic dispersions in such
clusters (e.g.,
Bothun 1981).
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